Cathy and Wendy had 820 buttons altogether. They decided to play a game. In the first round, Wendy lost 64 buttons to Cathy. In the second round, Cathy lost 38 buttons to Wendy. At the end of the two rounds, Wendy had thrice as many buttons as Cathy.

1. How many buttons did Cathy have in the end?
2. How many buttons did Wendy have at the beginning of the game?

	Cathy	Wendy	Total
Before	1 u + 38 - 64	3 u - 38 + 64	820
Round 1	+ 64	- 64
Round 2	- 38	+ 38
After	1 u	3 u	820

(a)
Total number of buttons
= 1 u + 3 u
= 4 u

4 u = 820

1 u = 820 ÷ 4 = 205

Number of buttons that Cathy had in the end
= 1 u
= 205

(b)
Working backwards.

Number of buttons that Wendy had at the end of round 2
= 3 u
= 3 x 205
= 615

Number of buttons that Wendy had at the end of round 1
= 615 - 38
= 577

Number of buttons that Wendy had at the beginning of the game
= 577 + 64
= 641

Answer(s): (a) 205; (b) 641